We have developed a self-consistent model for predicting velocity of 1/2[111] screw dislocation in binary iron--carbon alloys gliding by a high-temperature Peierls mechanism. The methodology of modelling includes: (i) Kinetic Monte-Carlo (kMC) simulation of carbon segregation in dislocation core and determination the total carbon occupancy of the core binding sites; (ii) Determination of kink-pair formation enthalpy of a screw dislocation in iron---carbon alloy; (iii) KMC simulation of carbon drag and determination of maximal dislocation velocity at which the atmosphere of carbon atoms can follow a moving screw dislocation; (iv) Self consistent calculation of average velocity of screw dislocation in binary iron--carbon alloys gliding by a high-temperature kink-pair mechanism under constant strain rate. We conduct a quantitative analysis of the conditions of stress and temperature at which screw dislocation glide in iron--carbon alloy is accomplished by a high-temperature kink-pair mechanism. We estimate the dislocation's velocity at which screw dislocation brakes away from the carbon cloud and thermally-activated smooth dislocation propagation is interrupted by sporadic bursts controlled by athermal dislocation activity.